VX-710 is an investigational agent which has been shown in animals to reverse cell resistance to paclitaxel. The primary objective of this study is to determine the efficacy of the combination of VX-710 with paclitaxel in the treatment of women with advanced ovarian cancer (including primary peritoneal or fallopian tube tumors) refractory to paclitaxel containing therapy. The secondary objective of this study is to further establish the tolerability and safety of VX-710 when administered in combination with paclitaxel, and to further establish the plasma pharmacokinetics of paclitaxel when used in combination with VX-710. VX-710 is to be administered at 120mg/m2/hr via central venous access device over 24 hours beginning 4 hours prior to the initiation of Taxol at 80 mg/m2 IV over 3 hours every 3 weeks. All patients may continue with treatment until disease progression or adverse effects prohibit further treatment. Those patients who achieve a complete response should receive at least 2 additional courses beyond complete response. Because of the required pharmacokinetic samples for course #1, all patients will receive their first treatment at the Clinical Research Center (CRC). For the first course only, blood and plasma samples will be drawn at baseline, at the end of the Taxol infusion, 2 hours after the end of Taxol, 7 hours after Taxol, 15 hours after Taxol, and 33 hours after the end of the Taxol infusions.